All above info is good and relevant. I would speculate that since you had sticky pins, that they got too hot on the first drive. New pads don't really need to be run-in anymore (some specific brands will say if they do). As
@Doubeleive stated, that is a good way to try and clean up any material that may have transferred.
Another thing to look at is the hub finish. If you have scaly corrosion on the face and don't clean it off, it can cause issues because the rotor doesn't sit true. Luckily based on the pics it looks like you got a box store painted brand? I would assume they will honor a 1 time replacement for vibration - just omit the frozen pin thing.
Lube the pins liberally, but make sure to use a pick to move the rubber seal and let the air put. If not, it can act as an air spring and keep pressure on the pads, not allowing for free wiggle room.
Try opening the bleeder on the caliper, then use channel locks to back the piston in. Note the ease of movement, or lack thereof, when retracting it. If its fails to go back somewhat easliky with good fluid flow from the bleeder, thats an indicator you may have a caliper that will stick.
Verify the piston boot isn't airbound either - small screw driver next to the boot will release the pressure. Hold caliper with bleeder upright and let fluid run until free of bubbles. Tap with small hammer as needed gently to encourage air to exit. Best to do with master cylinder cap off. You may have to do one or 2 pressure bleeds once reassembled if the pedal feels spongy.